Getting started with Topology

[MATHNEM]

Hi everybody,
Forgive me if this is not the right subforum but I didn't find another one more suitable.

I'm going to take a course in Topology next year and I've been looking for some papers in order to get started but I've found that there are differents approaches to this subject. Thus far I know two, one that introduces at the beginning the concept of metric space (which is, I guess, the most common) and the other one says it's better to go directly to the definition of a topological space so students don't get the wrong idea that every topological space is a metric space.

I'd like to read your points of view, which one do you think is better? why?

Thanks in advance.

 

[pka]

I've found that there are differents approaches to this subject. Thus far I know two, one that introduces at the beginning the concept of metric space (which is, I guess, the most common) and the other one says it's better to go directly to the definition of a topological space so students don't get the wrong idea that every topological space is a metric space.

Which approach one follows will depend on the student's background. The metric space approach is well suited to undergraduate mathematics. It appeals to those who are already comfortable with measurements like are found in analytic geometry and vector calculus.

Whereas, the straight topological space approach appeals to those who are already comfortable with say axiomatic geometry. This approach gives a truer picture of the actual abstract subject matter of topology.

 

[MATHNEM]

Well, I'm in my second year of college (majoring in Pure Math) and my background is not the one I would like to have so I guess I'm not ready to "attack" topological space notion without studying metric spaces before.

Thanks for replying and nice forum by the way.